The Discrete Planar L0-Minkowski Problem

By Alina Stancu. 2002

294 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computer Graphics and Computer-Aided Design

View Paper: https://www.semanticscholar.org/paper/855b2e546eed78bdd74e8bae4d23ae1684e09995

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In Applied Mathematics

In Computer Graphics and Computer-Aided Design

Citations in the corpus

An extension of Minkowski's theorem and its applications to questions about projections for measures (2016, background): “Böröczky, Lutwak, Yang, Zhang [9], [10], [11], Lutwak, Yang, Zhang [48], Lutwak, Oliker [43], Stancu [58], Huang, Liu, Xu [25]) asks whether a symmetric convex body K is uniquely defined by its cone volume measure 1 n hK(u)fK(u), where u ∈ Sn−1.”
Necessary subspace concentration conditions for the even dual Minkowski problem (2017, unknown): “The discrete, planar, even case of the logarithmic Minkowski problem, i.e., with respect to origin-symmetric convex polygons, was completely solved by Stancu [49, 50], and later Zhu [55] as well as Böröczky, Hegedűs and Zhu [6] settled (in particular) the case when K is a polytope whose outer nor”
Affine Moser–Trudinger and Morrey–Sobolev inequalities (2009, unknown): “, [12], [14], [27], [31], [32], [33] – [41], [44], [48] – [50]).”
A classification of $\operatorname{SL}(n)$ invariant valuations (2010, background): “For p > 1, Lp affine surface area was defined by Lutwak [39] as the notion corresponding to affine surface area in the Lp Brunn Minkowski theory (see [13], [14], [38]–[46], [57], and [58] for contributions to the Lp Brunn Minkowski theory).”
Local Lp-Brunn-Minkowski inequalities for p<1 (2017, background): “ttled in [6] in dimension n = 2; it remains open in full generality in dimension n ≥ 3 (see also [22] for the planar uniqueness question for smooth convex bodies with strictly positive curvature, and [63] for existence and uniqueness in the even planar problem when µ is assumed discrete). Various ot”
The discrete logarithmic Minkowski problem (2014, methodology): “[60] A. Stancu, The discrete planar L0-Minkowski problem.”
The dual Minkowski problem for negative indices (2017, methodology): “The uniqueness part of the logarithmic Minkowski problem, in general, remains open (see Böröczky-LYZ [8] and Stancu [42, 43] for results in the planar case).”
The dual Minkowski problem for symmetric convex bodies (2017, methodology): “[48] A. Stancu, The discrete planar L0-Minkowski problem, Adv.”
On the planar dual Minkowski problem (2018, background): “There is a vast body of literature concerning the planar Lp-Minkowski problem [1, 3, 5, 15, 18, 19, 20, 21, 48, 49, 50].”
General $L_p$ affine isoperimetric inequalities (2008, unknown): “, [7, 10, 11, 21, 24, 29–34, 40, 46–48].”
Cone-volume measure of general centered convex bodies (2016, unknown): “Stancu [40,41].”
The logarithmic Minkowski problem (2012, unknown): “1 was proved by Stancu [57].”